It''s for hardware funtionality. The single data line has to be bidirectional. That means the I/O pins on both ends of the single wire signal have to sometimes be input pins and sometimes output pins. By having a pull-up resistor wired to Vcc, then there will always be a valid logic level on the wire as pins switch modes.
It's the same reqirement needed for the clock and data lines on any I2C device wiring to an arduino.
PS: your example drawing figures 2 and 3 are electrical the same, aren't they? Anyway just wire the resistor between the voltage and the signal wire anywhere along the run or at either end.
Lefty